Evaluation of Isosteric Heat of Adsorption Clausius Clapeyron, Lecture notes of Chemistry

Download Evaluation of Isosteric Heat of Adsorption Clausius Clapeyron and more Lecture notes Chemistry in PDF only on Docsity! Article Isosteric Heat: Comparative Study between Clausius–Clapeyron, CSK and Adsorption Calorimetry Methods Liliana Giraldo 1, Paola Rodriguez-Estupiñán 2 and Juan Carlos Moreno-Piraján 2,* 1 Departamento de Química, Universidad Nacional de Colombia, Bogotá 11001, Colombia; lgiraldogu@unal.edu.co 2 Departamento de Química, Facultad de Ciencias, Universidad de los Andes, Bogotá 111711, Colombia; jp.rodrigueze@uniandes.edu.co * Correspondence: jumoreno@uniandes.edu.co; Tel.: +57-1-3394949 (ext. 2786) Received: 8 March 2019; Accepted: 4 April 2019; Published: 10 April 2019 Abstract: This work presents the calorimetric study of five adsorbents with different chemical and textural characteristics: MOF-199, MCM-41, SBA-15, activated carbon prepared from corn cob (GACKP) and graphite. These solids were used to establish the differences between isosteric heats evaluated by three different methods: Clausius–Clapeyron (C-C), Chakraborty, Saha and Koyama (CSK) and Adsorption Calorimetry (A-Cal). The textural characterization results show solids that have values of specific surface area between 2271 m2·g−1 for the MOF-199 and 5.2 m2·g−1 for the graphite. According to the results obtained for the isosteric heats for each sample, the magnitude varies depending on the coverage of the adsorbate and the textural characteristics of each adsorbent. Solids with an organized structure have isosteric heat values that are coincident among the three methods. Meanwhile, heterogeneous solids such as activated carbon values evaluated by the CKS and C-C have a high dispersion method regarding the adsorption calorimetry method. The results obtained show that the adsorption calorimetry, being a direct experimental measurement method, presents less dispersed data. At low quantities, the isosteric heat of nitrogen adsorption decreased in the order MOF-199, GACKP, MCM-41, SBA-15 and Graphite. The order for the isosteric heats values was coherent with the surface characteristics of each of the solids, especially with the pore size distribution. Finally, throughout the coverage examined in this work, the isosteric heats for nitrogen adsorption determined by adsorption calorimetry (A-Cal) were larger than the evaluated by C-C and CSK indirect methods of vaporization. According to the results, it is shown that the adsorption calorimetry allows values of the isosteric heats of adsorption with an error of less than 2% to be established and also reveals the complex nature of the heterogeneity or homogeneity of the adsorbent. Keywords: isosteric heats; adsorption calorimetry; CKS isosteric; Clausius–Clapeyron 1. Introduction A fundamental aspect of the thermodynamic study of surface processes is the determination of adsorption heat with good precision [1]. This variable is directly related to adsorbate–adsorbent interactions and the behavior of porous materials in applications such as gas storage and separation [2–5] and in technology for separation and purification of gas mixtures like Pressure swing adsorption (PSA) [5–7]. It has been established that the determinations of the heat effects associated with the adsorbate–adsorbent interactions are usually more sensitive to the adsorption isotherms [5,7] and for this reason some authors have proposed that carrying out a combination of heat Processes 2019, 7, 203 2 of 25 measurements and adsorption capacity will provide complementary information to understand gas adsorption processes [5]. Experimentally, two methods are used to evaluate the heat of adsorption [5,8]. The first one is the calorimetric method (usually called direct method), which directly evaluates the heat released when the adsorbate is in contact with the adsorbent and the other method is the isosteric (indirect method) in which a quantitative relationship between pressure and temperature is measured at a constant amount of the adsorbed substance and the adsorbent [5]. Isosteric measurements are usually used more than calorimetric measurements. Different reasons have been presented by the authors: some proposed that direct determination of heat effects is often complicated and more costly, particularly in non-environmental conditions [5]. While it is assumed that the approaches of direct and indirect methods should give identical results, often ambiguity is generated, mainly due to the definitions of the isotherms and the choice of different thermodynamic models to adjust the corresponding adsorption isotherms [5,8–11]. The experimental results of the isosteric heat are very sensitive to the conditions of the adsorption isotherms, particularly if the analysis of the data is available only for a limited number of temperatures [5]. Isosteric analysis often leads to inconsistencies or even erroneous conclusions under conditions that are not ideal [2,4] because the thermodynamic analysis is based on the numerical adjustment of the adsorption isotherms using semi-empirical models, such as Langmuir single-site or dual-site models [5,12,13], the Toth model [14–16] or the virial equation [17–20]. Although semi-empirical parameters can be correlated with a binding affinity between adsorbate and adsorbent [20], they are significant only in the context of specific isotherms [5]. As mentioned by Tian et al. [5,6,21–26], the correct determination of isosteric heat is fundamentally associated with defining the adsorbed phase. It was J. W. Gibbs who introduced this concept for heterogeneous systems in one of his first works in thermodynamics. From the point of view of the definitions of Gibbs to describe the properties of a surface and the interface, the latter can be represented as a two-dimensional dividing surface without any volume [5,21–30]; isosteric heat is often interpreted as the energy to transfer an adsorbate molecule from the bulk of the fluid phase to the adsorbed phase under some fixed thermodynamic conditions of the system such as temperature, total volume and amount of adsorbent [26–31]. Some authors have analyzed that the Gibbsian formalism predicts non-physical isosteric heat under maximum thermodynamic conditions of the adsorption isotherm. However, unlike bulk systems, the properties of the adsorbed phase cannot be defined only with the excess surface area for each component [23–26,28]. Gibbs thermodynamics predict a non-physical isosteric heat when the adsorption isotherm exhibits a maximum [5,28–37]. In summary, the isosteric heat of adsorption allows characterization of the surface properties of adsorbents, catalysts and other materials [1], provides information on the homogeneity and heterogeneity of materials, for example allows study of the degree of graphitization of carbons [2–6], the formation of liquid films [7], the formation of molecular multilayers on a surface and the evaluation the adsorption energy distribution (AED) [8,36,38]. The isosteric heats of adsorption for a specific adsorbate can be calculated by applying the Clausius–Clapeyron (C-C) equation on the isothermal data at two different temperatures the formal derivation of the C-C equation can be found in the work of Pan et al. [39]. However, the simplification of the heterogeneity in the adsorbate–adsorbent interaction and the modeling isotherms for analyzing the experimental data, fail to completely explain the ∆Hads across all the range of pressures [23,24]. Some authors in recent works [22,24–26] have developed very rigorous thermodynamic studies to deduce isosteric heat without inconsistencies and that can be used for practical applications [21,31,38]. Among other very interesting methods that have also been applied to assess isosteric heat, the outstanding work of Chakraborty et al. [23–26] should be mentioned, who developed a theory to determine the isosteric heat of adsorption between an adsorbate (vapor) and an adsorbent (solid) based on the thermodynamics of chemical equilibrium, Maxwell’s relations and the entropy of the adsorbed phase. They presented an equation to calculate the isosteric heat of adsorption by making an adjustment to the Clausius–Clapeyron equation. Processes 2019, 7, 203 5 of 25 2.2. Measurement and Characterization 2.2.1. Nitrogen Adsorption-Desorption Isotherms at −196 ◦C Nitrogen adsorption-desorption isotherms were obtained at −196 ◦C using a sortometer automatic apparatus IQ2, Quantachrome, Miami, FL, USA. The samples were degassed for 6 h under vacuum at 200 ◦C prior to any adsorption experiment. 2.2.2. Thermogravimetric Analysis (TGA) Differential thermal analysis (DTA) and thermal gravimetric (TG) were performed on a STA7000 Series Simultaneous Thermal Analyzer (STA) instrument, Hitachi™, (Tokyo, Japan). Approximately 10–20 mg of adsorbent was placed in a platinum crucible on the pan of a microbalance and then heated from room temperature up to 800 ◦C at a heating rate of 2 ◦Cmin−1 while being purged with argon at a flow rate of 100 mLmin−1 and constantly weighed. 2.2.3. Infrared Spectroscopy (FTIR) and XRD of Samples used in this Research Fourier transform infrared spectroscopy (FTIR) absorbance spectra of adsorbents synthesized were obtained through the KBr technique, with the analysis performed on a Nicolet™ iS™50 FT-IR spectrometer (Madison, WI, USA) in the wave number range of 400–4000 cm−1. On the other hand, Powder X-ray diffraction (XRD) (PXRD) patterns were recorded on an X-ray diffractometer (MiniFlex II, Rigaku, Japan) at 30 kV and 15 mA using Cu Kα (λ = 1.5418 Å) radiation, with a scanning speed of 4◦ min−1, a step size of 0.01◦ in 2 h, and scanning range of 3–40◦. 2.2.4. SEM of Adsorbents Analyses of the morphology, chemical composition and the elemental maps of the samples were conducted by JEOL JSM-7100FA field emission Scanning Electron Microscope equipped with an energy dispersive X-ray (EDX) system (Freising, Germany). 2.2.5. Differential Enthalpy Measurement by Adsorption Calorimetry The differential enthalpy of nitrogen adsorption measurements was obtained in a high sensitivity Tian-Calvet heat flow microcalorimeter. This equipment was designed and built in Porous Solids and calorimetry laboratory (Author’s Laboratory) [50,51]. Prior to each experiment, the samples were degassed at 250 ◦C and 1 × 10−6 MPa for 24 h. The microcalorimeter uses two calorimetric cells: the first one contains the sample, and the second one acts as a reference, it is usually empty. The experiments were conducted in an isothermal manner by gradually feeding increasing small doses of nitrogen over previously degassed samples. The initial dose sent to the system corresponded to a pressure of 10 mbar. Since the initial dose was sufficiently small, the heat obtained can be considered as a differential adsorption heat. A new dose of nitrogen (10 mbar) was then added until equilibrium pressure was achieved. Subsequently, the nitrogen dose was increased, and the procedure was repeated until no change in pressure was observed. This was achieved at around 35 bar (3.5 MPa). The adsorption pressures in the measurements were monitored with Baratron pressure transducers (Andover, MA, USA) to record low pressures and a Honeywell type Model HP High-Pressure Transducer (MKS Instrument, Andover, MA, USA) to record the changes at high pressures. The calorimeter allows sensing the heat generated by each dose added and the pressure drop in the cell allows obtaining the amount adsorbed. The calorimetric adsorption experiments finished when the released heat at a relatively high pressure and the increase in adsorbed amount were insignificant [52–55]. The calorimeter was calibrated electrically in order to establish its correct operation as well as to convert the voltage-time signal into units of energy. The constant established for this equipment was 25.4 ± 0.3 WV−1. Processes 2019, 7, 203 6 of 25 2.2.6. Evaluation of Isosteric Heat of Adsorption by Clausius–Clapeyron (C-C) The differential enthalpy of adsorption at constant coverage or what is known as the isosteric method can be evaluated by determining the isotherms in the lab at two or more different temperatures. Taking these isotherms as a starting point, it is possible to perform the respective data processing and relate them by means of a graphical representation the pressure logarithm, ln p, for a given amount adsorbed na as a function of the reciprocal temperature, 1/T. Then, using the Clausius–Clapeyron equation it is possible to establish the isometric heat of adsorption. It is usually assumed that there is no enthalpy or entropy variation with temperature. The thermodynamic expression used is: ∆ads . hna = R ( ∂ ln[P] ∂ 1T ) na , (1) where ∆ads . hna is the enthalpy of differential adsorption and R is the gas constant. Some authors affirm that it is possible to measure two isotherms with 10 K difference, i.e., for liquid nitrogen (77 K) and liquid argon (87 K); therefore, it is possible to relate the equilibrium pressures Pl and P2 to the corresponding temperatures T1 and T2 for a given amount adsorbed: ∆ads . h = RT1T2 T2 − T1 ln P2 P1 . (2) According to this, it is noteworthy that the accuracy of this type of calculation depends on the measurement of the pressure and eventually problems arise at low pressures. This is mainly due to the accuracy of the adsorbent-adsorbent balance and not to the pressure reading accuracy, because the pressure gauges are usually more than sufficient, especially in the case of the adsorbate load in the range of the micropores in materials that are poorly conductive, as in the case of silica: some authors have shown that a small deviation in equilibrium due to molecular diffusion or thermal transfer can generate a relatively large variation in pressure measurements [56]. This argument can in some cases explain the dispersion in the results obtained using the isosteric method. 2.2.7. Evaluation of the Isosteric Heats of Adsorption by Chakraborty-Saha-Koyama (CSK) The CSK model [24–26] proposes the calculation of the isosteric heat of adsorption using a series of thermodynamic arguments that allows obtaining an expression to evaluate this parameter (∆Hads). The development of this model can be found in Chakraborty et al. [24]. The fundamental expression taken from [24] is shown to contextualize the reader about the equation that was used to deduce the isosteric heat in this work. The CSK model obtains the expression of ∆Hads from the concepts of chemical equilibrium potentials between the gaseous and adsorbed phases and the state equation, as well as the Maxwell relationships, using these relationships and the chemical potential gradient of P and T with respect to entropy and specific volumes, respectively. The CSK model derives the expression ∆Hads to calculate the isosteric heat. Following the development of CSK, the following expression is obtained [24]: ∆ads ∼= TVg ( ∂P ∂ma ) T dma dT + RT2 [( ∂(ln P) ∂T ) ma ] = TVg ( ∂P ∂ma ) T dma dT + ∆Hads. (3) Vg: Specific volume of the gas T: Temperature P: Pressure ma: Adsorbate mass ∆Hads: Conventional form of Clausius–Clapeyron isosteric heat (C-C) Processes 2019, 7, 203 7 of 25 3. Results and Discussion 3.1. Porous Texture Analysis Table 1 shows the textural parameters determined by the N2 adsorption isotherms at −196 ◦C: apparent surface area, SBET, by the Brunauer–Emmett–Teller (BET) method [32]; (ii) Dubinin−Radushkevich (DR) micropore volume, VDR, [57,58]. Therein; (iii) total pore volume, V0.99, defined as the volume of liquid nitrogen corresponding to the amount adsorbed at a relative pressure P/P◦ = 0.99 [39,57,58]. The mesopores volume, Vme, was calculated as the difference V0.99−VDR. The average micropore diameter, L0, and adsorption energy, Eo, were also calculated [57–59], as well as the pore size distributions (PSD) by application of the Density Functional Theory (DFT) [39,56–59]. The samples have a wide range of textural properties, such as the apparent surface area ranging from 5.2 m2g−1 for graphite to 2271 m2g−1 for MOF-199. Most prepared samples are mainly microporous if one takes into account the ratio, VDR/V0.99, which varied from 0.83 to 094. The graphite does not have a porosity as expected. Table 1. Textural parameters of all samples from the N2 adsorption-desorption isotherm at −196 ◦C. Samples SBET(m2·g−1) V0.99 (cm3·g−1) VDR (cm3·g−1) Eo (kJ·mol−1) Lo (nm) VDR/V0.99 VMeso (cm3·g−1) MOF-199 2271 0.66 0.62 8.47 7.3 0.94 0.04 MCM-41 1274 0.44 0.40 3.58 8.4 0.91 0.04 SBA-15 663 0.24 0.17 5.41 6.2 0.83 0.07 GACKP 856 0.33 0.28 9.32 7.1 0.85 0.05 Graphite 5.2 0.10 - 7.25 0.3 - 0.001 Taking into account the scope of this work, the materials have a diversity in the textural properties which will allow analyzing the effect of these characteristics with respect to the evaluation of the isosteric heats using the three methods proposed in this investigation. Figure 1a shows the N2 adsorption-desorption isotherms at −196 ◦C for all the samples used in this study. The isotherm for the MCM-41 presents an isotherm type IV, characteristic of materials with a uniform cylindrical mesoporous system. It also presents a hysteresis loop of type H3, which corroborates the previous statement, because this type of hysteresis is characteristic of solid particles solid formed by cylindrical channels, aggregates (consolidated) or agglomerated (not consolidated) of spheroidal particles [60,61]. Processes 2019, 7, x FOR PEER REVIEW 7 of 25 average micropore diameter, L0, and adsorption energy, Eo, were also calculated [57–59], as well as the pore size distributions (PSD) by application of the Density Functional Theory (DFT) [39,56–59]. The samples have a wide range of textural properties, such as the apparent surface area ranging from 5.2 m2g−1 for graphite to 2271 m2g−1 for MOF-199. Most prepared samples are mainly microporous if one takes into account the ratio, VDR/V0.99, which varied from 0.83 to 094. The graphite does not have a porosity as expected. Taking into account the scope of this work, the materials have a diversity in the textural properties which will allow analyzing the effect of these characteristics with respect to the evaluation of the isosteric heats using the three methods proposed in this investigation. Figure 1a shows the N2 adsorption-desorption isotherms at −196 °C for all the samples used in this study. The isotherm for the MCM-41 presents an isotherm type IV, characteristic of mat rials with a uniform cylindrical mesoporous system. It also presents a hysteresis loop of type H3, which corroborates the previous statement, because this type of hysteresis is characteristic of solid particles solid formed by cylindrical channels, aggregates (consolidated) or agglomerated (not consolidated) of spheroidal particles [60,61]. It is interesting to note that the N2 adsorption isotherm of the MCM-41 shows three different steps. The first step (P/P° = 0.0–0.2) corresponds to monolayer-multilayer adsorption on the walls of the pores. The second step (P/P° = 0.2–0.3), resembles typical adsorption of a well-defined capillary condensation within the mesopores [34]. A very sharp step (third step) occurs between 0.3 and 0.4 P/P° is due to the uniform filling pores of the hexagonal lattice. The H3 hysteresis loop was observed between 0.4 and 1.0 P/P°. This loop is associated with the multilayer adsorption on the outer surface of the crystals [44,61]. As for the N2 adsorption isotherm corresponding to the SBA-15, it presents an isotherm type IV according to the IUPAC classification, which are typical for esoporous solids and presents a hysteresis loop type H1, which indicates the existence of mesopores and in this particular case of the two-dimensional hexagonal distributions of the pores, which are very characteristic of mesoporous SBA-15 atrices [62,63]. The isotherm shows an elongated inflection in the P/P° range of 0.40 to 0.70 characteristic of capillary condensation within uniform pores. (a) (b) Figure 1. N2 adsorption-desorption isotherms (a) and (b) pore size distributions by DFT models. Table 1. Textural parameters of all samples from the N2 adsorption-desorption isotherm at −196 °C. Samples SBET (m2·g−1) V0.99 (cm3·g−1) VDR (cm3·g−1) Eo (kJ·mol−1) Lo (nm) VDR/V0.99 VMeso (cm 3·g−1) MOF-199 2271 0.66 0.62 8.47 7.3 0.94 0.04 MCM-41 1274 0.44 0.40 3.58 8.4 0.91 0.04 SBA-15 663 0.24 0.17 5.41 6.2 0.83 0.07 GACKP 856 0.33 0.28 9.32 7.1 0.85 0.05 Graphite 5.2 0.10 - 7.25 0.3 - 0.001 i r . 2 adsorption-desorption isother s (a) and (b) pore size distributions by F o els. Processes 2019, 7, 203 10 of 25 Table 2. Mean error adjustments between different surface textures (NLDFT vs. QSDFT) in pores slit and slit/cylindrical for the samples prepared in this research. Sample NLDFT QSDFT Fitting Error (Slit Pore) (%) Fitting Error (Cyl. Pore) (%) Fitting Error (Combined) (%) Fitting Error (Slit Pore) (%) Fitting Error (Cyl. Pore) (%) Fitting Error (Combined) (%) Graphite 5.296 6.819 6.819 4.364 7.510 7.510 MOF-199 0.600 0.140 0.135 0.840 0.700 0.698 SBA-15 - 0.513 - - - - GACKP 0.499 0.335 0.300 0.138 0.057 0.030 MCM-41 - 3.100 - - - - 3.2. Thermogravimetric (TG) Analysis of Samples The thermogravimetric analysis (TGA) for each of the samples was carried out in order to analyze its thermal stability. The TG and DTG of the solids under study are shown in Figure 3a,b. The TG/DTG of the MOF-199 presents two thermal events: the first observed weight loss (~9.5%) is below 200 ◦C and is attributed to the removal of remaining solvent and desorption of water molecules. The second weight of about ~38% occurred at ~300–380 ◦C, which is related to the decomposition of the organic linker group, benzentricarboxylic acid. After this temperature, the observable thermal events do not reveal significant changes, which indicates the formation of CuO, which takes place above 350 ◦C [68]. The TGA of the MCM-41 is also presented in Figure 3. The weight loss of 9.1% due to physisorbed water molecules, after that, the dehydroxylation of the Si-OH groups occurs continuously well above 100 ◦C and respective mass losses are not evidenced. On the basis of anhydrous silica, the concentration of Si-OH groups bound to hydrogen is approximately 2.1/nm2 [69]. Processes 2019, 7, x FOR PEER REVIEW 10 of 25 Table 2. Mean error adjustments between different surface textures (NLDFT vs. QSDFT) in pores slit and slit/cylindrical for the samples prepared in this research. Sample NLDFT QSDFT Fitting Error (Slit Pore) (%) Fitting Error (Cyl. Pore) (%) Fitting Error (Combined) (%) Fitting Error (Slit Pore) (%) Fitting Error (Cyl. Pore) (%) Fitting Error (Combined) (%) Graphite 5.296 6.819 6.819 4.364 7.510 7.510 MOF- 199 0.600 0.140 0.135 0.840 0.700 0.698 SBA-15 - 0.513 - - - - GACKP 0.499 0.335 0.300 0.138 0.057 0.030 MCM-41 - 3.100 - - - - 3.2. Thermogravimetric (TG) Analysis of Samples The thermogravimetric analysis (TGA) for each of the samples was carried out in order to analyze its thermal stability. The TG and DTG of t e solids und r study ar show in Figure 3 ,b. The TG/DTG of the MOF-199 presents two thermal ev nts: the first bserved weight loss (~9.5%) is below 200 °C and i a tributed to th removal of remaining solvent and desorption f water molecules. The second weight of about ~38% occurred at ~300–380 °C, which is r lated to the decomposition of the organic linker group, benzentricarboxylic acid. After thi temperature, the observable thermal vents d not reveal significant changes, which indicates the formation of CuO, which takes place above 350 °C [68]. The T f the MCM-41 is also presented in Figure 3. The weight loss of 9.1% due to physisorbed water molecules, after that, the de ydroxylati n of the Si-OH groups occurs continuously well above 100 °C nd respective mass losses are not evidenced. On the basis of anhydrous silica, the concentration of Si-OH groups bound to hydrogen is approximately 2.1/nm2 [69]. (a) (b) Figure 3. (a) TGA and (b) DTG of MOF-199, MCM-41, SBA-15, GACKP and Graphite. The TGA of the SBA-15 (Figure 3) shows a weight loss below 95 °C of approximately 7%, due to the physical removal of water molecules adsorbed, while the soft weight loss presented in the range of 100–700 °C, might be associated with the decomposition of the surfactant into the pores and the condensation of silanol groups on the surface to form siloxane at higher temperatures [70]. The TGA of the GACKP is shown in Figure 3. There, a loss of mass of 4.5% below 100 °C can be observed, which indicates the humidity of the GACKP sample. Between 180 and 800 °C, a continuous mass loss (12%) is observed related to the decomposition of the solid in CO2 and CO because the carbonaceous surfaces are normally oxidized, which is why the mass loss can be associated to the Figure 3. (a) TGA and (b) DTG of MOF-1 9, MCM-41, SBA-15, GACKP and Graphite. The TGA of the SBA-15 (Figure 3) shows a weight lo s below 95 ◦C of a proximately 7%, due to the physical removal of water molecules adsorbed, while the soft weight loss presented in the range of 1 0–7 0 ◦C, might be associated with the decompos tion of the surfactant into the pores and the condensation of silanol groups on the surface to form siloxane at higher temperatures [70]. The TGA of the GACKP i shown in Figure 3. There, a lo s of ma s of 4.5% below 1 0 ◦C can be observed, which indicates the humidity of the GACKP sample. Betw en 180 and 8 0 ◦C, a continuous mass loss (12%) is observed related to the decompos tion of the solid in CO2 and CO because the carbonaceou surfaces are normally oxidized, which is why the mass loss can be a sociated to the decomposition of the surface carbon-oxygen compounds. It is worth noting that the TG/DTG profiles corresponding to this sample are very clear and simple compared to other solids obtained from Processes 2019, 7, 203 11 of 25 lignocellulosic residues, which indicates that the combined activation with phosphoric acid and KOH allows the formation of thermally stable carbonaceous structures. The TG/DTG corresponding to the graphite can be seen in Figure 3a,b, showing that the solid begins to lose weight at approximately 570 ◦C, suggesting the decomposition of the surface carboxyl compounds in graphite structure at this temperature. 3.3. XRD and FTIR Analysis of Samples The purity of the crystalline phase of MOF-199 was confirmed by XRD powder analysis. The diffraction peaks of MOF-199 were consistent with the theoretical patterns of the single crystal data and those previously reported in the literature. In addition, the XRD reflections of the CuO derived from the MOF exhibit pure phase nature without any phase of impurities such as Cu, Cu2O and Cu(OH)2 [16,71–73] (Figure 4a). Processes 2019, 7, x FOR PEER REVIEW 11 of 25 decomposition of the surface carbon-oxygen compounds. It is worth noting that the TG/DTG profiles corresponding to this sample are very clear and simple compared to other solids obtained from lignocellulosic residues, which indicates that the combined activation with phosphoric acid and KOH allows the formation of thermally stable carbonaceous structures. The TG/DTG corresponding to the graphite can be seen in Figure 3a,b, showing that the solid begins to lose weight at approximately 570 °C, suggesting the decomposition of the surface carboxyl compounds in graphite structure at this temperature. 3.3. XRD and FTIR Analysis of Samples The purity of the crystalline phase of MOF-199 was confirmed by XRD powder analysis. The diffraction peaks of MOF-199 were consistent with the theoretical patterns of the single crystal data and those previously reported in the literature. In addition, the XRD reflections of the CuO derived from the MOF exhibit pure phase nature without any phase of impurities such as Cu, Cu2O and Cu(OH)2 [16,71–73] (Figure 4a). The obs rved reflections are adjusted according to a mono linic s ructure with the space group C2/c. The values of the reticular structure parameters were calculated from Rietveld r finement an were found to b a = 4682 (7), b = 3427 (6), c = 5132 (2) and β = 99,322, wh ch are consistent with the values in the literature (JCPDS Card no.48–1548). The average value of the crystallite size is also found (a) (b) Figure 4. (a) XRD of MOF-199 and Graphite; (b) XRD of MCM-41, SBA-15 and GACKP. The peaks of absorption at approximately 1650, 1565 and 1380 cm−1 were assigned to the vibrations characteristic of groups C=O, the peaks at approximately 1445 cm−1 were attributed to the stretching of C=C in the benzene ring [74] and the peaks at approximately 670 cm−1 are related to the stretching vibrations of Cu-O [75]. In addition, the wide peak around 3435 cm-1 in the FTIR spectrum of MOF-199 could be assigned to the vibration of -OH groups and coordinated or uncoordinated water molecules [76]. The XRD diffractograms (X-ray diffraction) for the sample of MCM-41, are shown in Figure 4b. Regarding the XRD of the MCM-41, the peaks attributed to this structure were also detected for the support synthesized at 2.1° and 3.5°, which correspond to the diffraction planes (1 0 0) and (2 0 0) of this material [62]. When examining the XRD at greater angles (Figure 4b), the presence of amorphous SiO2 (broad diffraction peak around 26.3 °) is clearly observed. The FTIR corresponding to the MCM-41 sample prepared for this study is shown in Figure 5a. The spectrum shows characteristic bands at 1110 and 825 cm−1 that can be assigned to the asymmetric and symmetric stretching vibration modes of the Si-O-Si species, respectively [77,78]. A band towards 980 cm−1 can be attributed to the tension of the Si-OH bonds present in the sample MCM-41. The XRD patterns for SBA-15 are shown in Figure 4b. The sample of the SBA-15 shows a large wide peak between 2θ = 12 and 32 Å which shows that it is amorphous nature. The two reflections of Figure 4. (a) XRD of MOF-199 and Graphite; (b) XRD of C -41, SB -15 and P e observed reflections are adjusted according to a monoclinic structure with the space group C2/c. The values of the reticular structure par meters were calculated from Rietveld refinement and were found to be a = 4682 (7), b = 3427 (6), c = 5132 (2) and β = 99,322, which are consistent with t values in the literature (JCPDS Card no.48–1548). The average val e of the crystallite size is also fo nd at 21 nm according to the Scherrer equation [73]. The peaks of absorption at approximately 1650, 1565 and 1380 cm−1 were assigned to the vibrations characteristic of groups C=O, the peaks at approximately 1445 cm−1 were attributed to the stretchi of C=C in the benzene ring [74] and the peaks at approximately 670 cm−1 ar related to t e stretching vibrations of Cu-O [75]. In addition, the wide peak around 3435 cm-1 in the FTIR spectrum of MOF-199 could be assigned to the vibration of -OH groups and coordinated or uncoordinated water molecules [76]. e XRD diffract grams (X-ray diffraction) for the sample f MCM-41, are shown in Figure 4b. Regarding the XRD of the MCM-41, the peaks attributed to this structure were als detected for the support synthe ized at 2.1◦ and 3.5◦, which correspond to th diffraction planes (1 0 0) (2 0 0) of this aterial [62]. When examining the XRD at greater a gles (Figure 4b), the presence of amorphous SiO2 (broad diffraction peak around 26.3◦) is clearly observed. The FTIR corresponding to the MCM-41 sample prep red for this st dy is shown in Figure 5a. The spectrum shows characteristic bands at 1110 and 825 cm−1 that can be assigned to the asymmetric and symmetric stretching vibration modes of the Si-O-Si species, respectively [77,78]. A band towards 980 cm−1 can be attributed to the tension of the Si-OH bonds present in the sample MCM-41. The XRD patterns for SBA-15 are shown in Figure 4b. The sample of the SBA-15 shows a large wide peak between 2θ = 12 and 32 Å which shows that it is amorphous nature. The two reflections of Processes 2019, 7, 203 12 of 25 Brag corresponding to peaks (1 1 0) and (2 0 0) at the mid-range of the 2-theta angle suggest that these materials have highly ordered hexagonal mesostructures in 2-D [79]. The FTIR spectrum of the SBA-15 are presented in Figure 5a. In the spectrum, two strong absorption peaks are observed at 1100 and 820 cm−1 assigned to the asymmetric and symmetric vibration modes of the inorganic framework Si-O-Si [80]. The characteristic band of the Si-OH stretch mode is around 970 cm−1. These bands corroborate the chemical nature of the SBA-15 and its satisfactory synthesis. Additionally, the FTIR spectrum of SBA-15 showed a wide and intense peak at 3550–3350 cm−1, which was assigned to the silanol group (Si-OH) or "networks" of silanol with crossed hydrogen bonds [76]. The XRD patterns for GACKP present (Figure 4b) two broad peaks around 12◦ and 25◦ corresponding to (0 0 2) and (1 0 0) planes, respectively [66]. This type of behavior is in good agreement with other reported results for this type of solids and the amorphous nature of the sample. Figure 5b shows the FTIR spectrum of GACKP scanning from 400 to 4000 cm−1. The observed O-H stretching around 3445 cm−1 was attributed mainly to chemisorbed water molecules and hydroxyl groups on the surface of the material. On the other hand, the stretch corresponding to C-H was observed around 2950 cm−1. The bands located around 1650 cm−1 are assigned to the characteristic olefin group (-C = C-), which suggests that some graphitization is presented for the GACKP sample [81]. With respect to the XRD patterns of the graphite in Figure 4a, it is observed that the material is highly structured and organized. This can be verified by seeing the good definition of the peaks and the high resolution of the peak (0 0 2), at an angle of 2θ corresponding to 26.3◦ (KαCu). This value corresponds to an interatomic distance (d002) of 3.36 Å. Figure 5b shows the FTIR corresponding to the graphite sample used in this study. The spectrum is characteristic of a sample of this type widely reported and analyzed in the scientific literature. The approximate band at 3410 cm−1 is attributed to the -OH stretch vibration of hydroxyl groups and water molecules [79]. The bands centered at 1750–1710 cm−1 correspond to the stretching vibrations C=O of the carbonyl and carboxylic groups [36,59]. The bands located at 1620–1630 cm−1 resulted from the C=C stretching mode of the graphitic domains without oxidation [8]. In addition, the peaks attributed to the deformation vibration of the tertiary C-OH groups appeared at 1400 cm−1 [38,82]. The peaks located at approximately 1225 and 1080 cm−1 correspond to the stretching vibrations of C-O-C and C-O, respectively [82–85]. Processes 2019, 7, x FOR PEER REVIEW 12 of 25 Brag corres o i g to eaks (1 1 0) a (2 0 0) at the mid-range of the 2-theta angle suggest that these aterials ave ig ly or ere exago al esostr ct res i 2- [79]. The F I s ectr of t e S -15 are rese te i Fig re 5a. In the s ectru , t o stro g absorption peaks are observe at 1100 an 820 c 1 assigned to the asy etric an sy etric vibration o es of the inorganic fra e ork Si- -Si [80]. The characteristic ban of the Si- stretch ode is aroun 970 c 1. These bands corroborate the chemical nature of the SBA-15 and its satisfactory synthesis. Additionally, the FTIR spectrum of SB -15 sho ed a ide and intense peak at 3550–3350 c −1, which was assigned to the silanol group (Si-OH) or "networks" of silanol ith crossed hydrogen bonds [76]. The patterns for P present (Figure 4b) t o broad peaks around 12° and 25° corresponding to (0 0 2) and (1 0 0) planes, respectively [66]. This type of behavior is in good agreement with other reported results for this type of solids and the amorphous nature of the sample. Figure 5b shows the FTIR spectrum of GACKP scanning from 400 to 4000 cm−1. The observed O-H stretching around 3445 cm−1 was attributed mainly to chemisorbed water molecules and hydroxyl groups on the surface of the material. On the other hand, the stretch corresponding to C-H was observed around 2950 cm−1. The bands located around 1650 cm−1 are assigned to the characteristic olefin group (-C = C-), which suggests that some graphitization is presented for the GACKP sample [81]. With respect to the XRD patterns of the graphite in Figure 4a, it is observed that the material is highly structured and organized. This can be verified by seeing the good definition of the peaks and the high resolution of the peak (0 0 2), at an angle of 2θ corresponding to 26.3° (KαCu). This value corresponds to an interatomic distance (d002) of 3.36 Å. Figure 5b shows the FTIR corresponding to the graphite sample used in this study. The spectrum is characteristic of a sample of this type widely reported and analyzed in the scientific literature. The approximate band at 3410 cm−1 is attributed to the -OH stretch vibration of hydroxyl groups and water molecules [79]. The bands centered at 1750– 1710 cm−1 correspond to the stretching vibrations C=O of the carbonyl and carboxylic groups [36,59]. The bands located at 1620–1630 cm−1 resulted from the C=C stretching mode of the graphitic domains without oxidation [8]. In addition, the peaks attributed to the deformation vibration of the tertiary C- OH groups appeared at 1400 cm−1 [38,82]. The peaks located at approximately 1225 and 1080 cm−1 correspond to the stretching vibrations of C-O-C and C-O, respectively [82–85]. (a) (b) Figure 5. (a) FTIR spectra of MOF-199, MCM-41 and SBA-15; (b) FTIR spectra of GACKP and Graphite. 3.4. SEM-EDX Analysis Figure 6(a1) shows the scanning electron microscopy (SEM) for the MOF-199 where there are some characteristics of small particles such as solids. In Figure 6(a2), as expected, the SEM micrograph for MOF-199 showed that a highly crystalline material was obtained (Figure 6a). The MOF-199 crystals in the SEM images have a double-sided pyramidal shape with a width of approximately 10–20 μm. Figure . (a) FTIR spectra of MOF-199, MC -41 and SBA-15; (b) FTIR spectra of GACKP and Graphite. 3.4. SEM-EDX Analysis Figure 6(a1) shows the scanning electron microscopy (SEM) for the MOF-199 where there are some characteristics of small particles such as solids. In Figure 6(a2), as expected, the SEM micrograph for MOF-199 showed that a highly crystalline material was obtained (Figure 6a). The MOF-199 crystals in the SEM images have a double-sided pyramidal shape with a width of approximately 10–20 µm. The SEM of sample MCM-41 is presented in Figure 6b. The morphology is similar to the material described in the literature as "wormy" MCM-41 [12]. The SEM images show slightly elongated particles Processes 2019, 7, 203 15 of 25 thermal behavior of the isostere on a heterogeneous surface [22,31,33]. In this area the values evaluated by the three methods are very similar, however, with the low standard deviation of the adsorption calorimetry (A-Cal), it is observed that the indirect methods always underestimated the heat. In the area where the plateau is reached, which ranges from 1 to 3.5 mmol·g−1, corresponds to isosteric heats that occur on homogeneous surfaces [22,31]. Subsequently, there is an increase in the enthalpic value of isosteric heat of −32 to −48 kJ·mol−1, which is probably due to interactions of the N2 molecule within the porous structure of MOF-199. In this zone, the values calculated by C-C and CSK are below with respect to the direct measurement method using the adsorption calorimetry methodology. As mentioned above, the low standard deviation of the adsorption calorimetry allows differentiation of the heat released in the adsorption with respect the calculated ones. The adjustment of each of the methods used to calculate the isosteric heats is dependent on the porosity of the MOF. The isosteric heat of the experiment decreases with the coverage to the condensation step.Processes 2019, 7, x FOR PEER REVIEW 15 of 25 (a) MOF-199 (b) MCM-41 20 25 30 35 40 45 50 55 0 1 2 3 4 5 6 7 q s t,k Jm ol -1 Coverage, mmolg-1 A-Cal CSK C-C 0 5 10 15 20 25 30 0 1 2 3 4 5 q s t,k Jm m ol -1 Coverage, mmolg-1 A-Cal CSK C-C Figure 7. Cont. Processes 2019, 7, 203 16 of 25 Processes 2019, 7, x FOR PEER REVIEW 16 of 25 (c) SBA-15 (d) GACKP 0 5 10 15 20 25 30 0 1 2 3 4 5 q s t,k Jm m ol -1 Coverage, mmolg-1 A-Cal CSK C-C 0 5 10 15 20 25 30 35 40 0 2 4 6 8 10 q s t,k Jm ol -1 Coverage,mmolg-1 A-Cal CSK C-C Figure 7. Cont. Processes 2019, 7, 203 17 of 25 Processes 2019, 7, x FOR PEER REVIEW 17 of 25 (e) Graphite Figure 7. Isosteric heats of adsorption for N2. (a) MOF-199; (b) MCM-41; (c) SBA-15; (d) GACKP; (e) Graphite. Figure 7a shows the isosteric heats of MOF-199. The figure presents curves with very similar behavior: initially, they decay from approximately a value of −48 kJ·mol−1 to a value of −27 kJ·mol−1 where later they reach a plateau. This zone is very characteristic for solids of this type and is typical of thermal behavior of the isostere on a heterogeneous surface [22,31,33]. In this area the values evaluated by the three methods are very similar, however, with the low standard deviation of the adsorption calorimetry (A-Cal), it is observed that the indirect methods always underestimated the heat. In the area where the plateau is reached, which ranges from 1 to 3.5 mmol·g−1, corresponds to isosteric heats that occur on homogeneous surfaces [22,31]. Subsequently, there is an increase in the enthalpic value of isosteric heat of −32 to −48 kJ·mol−1, which is probably due to interactions of the N2 molecule within the porous structure of MOF-199. In this zone, the values calculated by C-C and CSK are below with respect to the direct measurement method using the adsorption calorimetry methodology. As mentioned above, the low standard deviation of the adsorption calorimetry allows differentiation of the heat released in the adsorption with respect the calculated ones. The adjustment of each of the methods used to calculate the isosteric heats is dependent on the porosity of the MOF. The isosteric heat of the experiment decreases with the coverage to the condensation step. The results of the isosteric heats obtained for the MCM-41 are presented in Figure 7b. In the diagrams it can be clearly seen that during the initial region where the first layer of the adsorbate is formed, the isosteric heat changes according to the method used to evaluate it, A-Cal and the CSK and C-C, and they are not coincident, because the confidence intervals for each method are significantly different (deviation bars in the figure). It is likely that the differences between the two calculation methods and the experimental one (adsorption calorimetry) can be attributed to the mechanism of N2 adsorption on a mesostructured porous network like the MCM-41 surface. The C- C and CSK methods by their nature of the determination do not contemplate the heterogeneity of the surface. Adsorption calorimetry, because it is a direct measurement method, can be recorded because it directly measures the thermal effect generated as the coating is made with the N2 molecules at that temperature. This zone is between 0.5–2.5 mmolg−1 where isosteric heat decrease to values close to −12 kJmol−1. Despite this, we observed that the heats are comparable between those evaluated by the CSK and C-C methods and the A-Cal method in the multilayer zone and the condensation step. 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 q s t,k Jm ol -1 Coverage,mmol-1 A-Cal CSK C-C Figure 7. Isosteric heats f ti n for N2. (a) MOF-199; (b) CM-41; (c) SBA-15; (d) GACKP; (e) Graphite. The results of the isosteric heats obtained for the MCM-41 a presented in Figure 7b. In the diagrams it can be clearly seen that during the initi l region where the first layer of the adsorbate is formed, the isosteric heat changes according to the method used to evaluate it, A-Cal and the CSK and C-C, and they are not coincident, because the confidence intervals for each method are significantly different (deviation bars in the figure). It is likely that the differences between the two calculation methods and the experimental one (adsorption calorimetry) can be attributed to the mechanism of N2 adsorption on a mesostructured porous network like the MCM-41 surface. The C-C and CSK methods by their nature of the determination do not contemplate the heterogeneity of the surface. Adsorption calorimetry, because it is a direct measurement method, can be recorded because it directly measures the thermal effect generated as the coating is made with the N2 molecules at that temperature. This zone is between 0.5–2.5 mmolg−1 where isosteric heat decrease to values close to −12 kJmol−1. Despite this, we observed that the heats are comparable between those evaluated by the CSK and C-C methods and the A-Cal method in the multilayer zone and the condensation step. Subsequently, the isosteric heats present a slight increase that may be associated with interactions between molecules of N2 into the pore system. The isosteric heats corresponding to the SBA-15 sample ar presented in Figure 7c. This Figure presents three well-differentiated areas, like this: the first one starts at a value of −25 kJ·mol−1 and falls to −2 kJ·mol−1, this zone c rrespo ds to the adsorption of N2 molecules on the homogeneous surface of SBA-15. When comparing the results obtained by the CSK and C-C methods it is possible to observe some inconsi te cies betwe n the calculated heats. The differ nt mechanism that involves the N2 adsorption in silica micropores and mesopores clearly affects the modeling of the experimental data with the indirect methods, but there is a better description of the adsorption process from the values obtained directly by the adsorption calorimetry method. This demonstrates the sensitivity of the calorimetric method to directly measure such effects. The next zone corresponds to a false plane followed by a wavy section that is assigned to the interaction with a surface of homogeneous characteristics; this value is between 4.5 and 6.6 mmolg−1 of N2 coverage. In this area, the experimental points tend to coincide better. However, it is clear that the adjustments of the results are subject to the textural distribution of each solid. Processes 2019, 7, 203 20 of 25 4. Conclusions A set of porous solids with different textural properties were characterized by N2 isotherms and XRD. Among the main findings are the disorganized structure and surface heterogeneity established by the activated carbon sample, while, graphite and mesostructured silicas seem to have a homogeneous surface related to the morphology of the pores that compose them, the slits and cylinders, respectively. For MOF-199, a combined geometry described better de N2 adsorption experimental data. From the chemical characterization with FTIR and TG-DTG, it is possible to study the chemical nature of the samples, evidencing the different oxygen-complex surfaces and amphoteric character of the carbonaceous and siliceous surfaces. Additionally, the great hydration capacity of the MOF-199. The TG-DTG analysis was also useful to establish the appropriate degasification temperature for the calorimetry and the adsorption isotherms The comparison of the isosteric heats obtained from every method shows a relationship of the nitrogen adsorption heats with the specific properties of each solid. It was established from the graphics obtained, that the heats that are released respond to a different interactions due to the porosity and chemical nature of the solid. It is evidenced by the different shapes and zones found, which are a function of their structure and surface homogeneity or heterogeneity as follows: The sequences of measured magnitude for the isosteric heats oscillate between ~−48 kJmol−1 (MOF-199) and ~−14 kJmol−1 (graphite), which correspond to physical interactions between the nitrogen molecules and the considered adsorbents. The use of the CSK and C-C methods present acceptable coherence, particularly for the MOF-199 and MCM-41 samples. However, for the samples which possess a more heterogeneous structure (such as SBA-15, GACKP), the methods mentioned above present great dispersion in their individual results, as well as when they are compared one to the other. In this work, the isosteric heats of nitrogen adsorption on microporous materials measured directly using adsorption calorimetry was compared with those obtained using the indirect adsorption isosteric method, according to Clausius–Clapeyron equation and the equation modified by CSK so as to establish the reliability, limitations and assumptions of the methods. In general, for all porous solids employed, we found a very good agreement between the isosteric heats measured using the adsorption calorimetry and the adsorption isosteric method throughout the range of coverage studied. Therefore, we can conclude that the use of the simpler technique, i.e., adsorption isosteric method together with simple assumptions leads to reliable results for isosteric heats. At low quantities, the isosteric heat of nitrogen adsorption decreases in the order MOF-199, GACKP, MCM-41, SBA-15 and Graphite. The order of isosteric heats is coherent with the surface characteristics of each of the solids, especially with the pore size distribution. Finally, throughout the coverage of nitrogen examined in this work, the isosteric heats evaluated by adsorption calorimetry are larger than the evaluated by C-C- and CSK indirect methods of vaporization. Author Contributions: Conceptualization, L.G. and J.C.M.-P.; methodology, L.G., J.C.M.-P. and P.R.-E.; formal analysis, L.G. and J.C.M.-P.; investigation, L.G. and J.C.M.-P.; data curation, L.G. and J.C.M.-P.; writing—original draft preparation, L.G. and J.C.M.-P.; writing—review and editing, L.G., J.C.M.-P. and P.R.-E.; visualization, L.G., J.C.M.-P. and P.R.-E. Funding: This research received no external funding. Acknowledgments: The authors thank the Framework Agreement between the Universidad de los Andes and the Universidad Nacional de Colombia and the act of agreement established between the Chemistry Departments of the two universities. The authors also appreciate the grant for funding research programs for Associate Professors, Full Professors, and Emeritus Professors announced by the Faculty of Sciences of the University of the Andes, 20-12-2019-2020, 2019, according to the project “Enthalpy, free energy and adsorption energy of activated carbon interaction and solutions of emerging organic compounds”. Conflicts of Interest: The authors declare no conflict of interest. Processes 2019, 7, 203 21 of 25 References 1. Myers, A.L. Thermodynamics of adsorption in porous materials. AIChE J. 2002, 48, 145–160. [CrossRef] 2. Bhatia, S.K.; Myers, A.L. Optimum conditions for adsorptive storage. Langmuir 2006, 22, 1688–1700. [CrossRef] 3. Lee, S.-J.; Bae, Y.-S. Can Metal-Organic Frameworks attain new DOE targets for on-board methane storage by increasing methane heat of adsorption? J. Phys. Chem. C 2014, 118, 19833–19841. [CrossRef] 4. Amrouche, H.; Creton, B.; Siperstein, F.; Nieto-Draghi, C. 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